A uniform cylindrical pop (soda) can of mass 0.140 kg is 12.0 cmtall and filled

Question

A uniform cylindrical pop (soda) can of mass 0.140 kg is 12.0 cmtall and filled with
1.31kg of pop (soda). Small holes are drilled in the top and bottomto drain the pop
(soda).
a)What is the height h of the center of mass of the system (system= the can and its
contents) as a function of the x, where x is the height of the pop(soda) level remaining
within the can?
b) What are the maximum and minimum values for h (i.e. what is hwhen the can is full and empty)?
c) What is the smallest value of h that occurs while the can isdraining?

Explanation / Answer

A) Center of mass of cylindrical empty can will be at half of theheight. i.e. Cm = 6 cm Now, Soda also will have center of mass at half the height. Let current remaining height = x cm Then Centre of Mass = x/2 cm Mass of soda left : 1.31 * (x/12) Therefore center of mass (h)= (.14 * 6 + x/2 * 1.31 *x/12)/(1.31* x/12 + .14) B) put x = 0 and x = 12 to get both values C) Differentiate above expression to get maximum and minimumvalues.

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